Geometry Internet Sites for further study
|
ASE MA 4: Geometry, Probability, and Statistics |
||
|
MA.4.1 Geometry: Understand congruence and similarity. |
||
|
Objectives |
What Learner Should Know, Understand, and Be Able to Do |
Teaching Notes and Examples |
|
MA.4.1.1 Experiment with transformations in a plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Example: How would you determine whether two lines are parallel or perpendicular? |
A point has position, no thickness or distance. A line is made of infinitely many points, and a line segment is a subset of the points on a line with endpoints. A ray is defined as having a point on one end and a continuing line on the other. An angle is determined by the intersection of two rays. A circle is the set of infinitely many points that are the same distance from the center forming a circular are, measuring 360 degrees. Perpendicular lines are lines in the interest at a point to form right angles. Parallel lines that lie in the same plane and are lines in which every point is equidistant from the corresponding point on the other line. |
Definitions are used to begin building blocks for proof. Infuse these definitions into proofs and other problems. Pay attention to Mathematical practice 3 “Construct viable arguments and critique the reasoning of others: Understand and use stated assumptions, definitions and previously established results in constructing arguments.” Also mathematical practice number six says, “Attend to precision: Communicate precisely to others and use clear definitions in discussion with others and in their own reasoning.”
Experiment with Transformations in a Plane https://www.virtualnerd.com/common-core/hsf-geometry/HSG-CO-congruence/A
|
|
MA.4.1.2 Prove theorems involving similarity. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. |
Students use similarity theorems to prove two triangles are congruent. Students prove that geometric figures other than triangles are similar and/or congruent. |
Solve Problems using Congruence and Similarity
https://www.illustrativemathematics.org/HSG
|
|
|
||
|
MA.4.2 Geometric Measure and Dimension: Explain formulas and use them to solve problems and apply geometric concepts in modeling situations. |
||
|
Objectives |
What Learner Should Know, Understand, and Be Able to Do |
Teaching Notes and Examples |
|
MA.4.2.1 Explain perimeter, area, and volume formulas and use them to solve problems involving two- and three-dimensional shapes. |
Use given formulas and solve for an indicated variables within the formulas. Find the side lengths of triangles and rectangles when given area or perimeter. Compute volume and surface area of cylinders, cones, and right pyramids. |
Geometry Lesson Plans https://www.learnnc.org/?standards=Mathematics--Geometry Example: Given the formula |
|
MA.4.2.2 Apply geometric concepts in modeling of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). |
Use the concept of density when referring to situations involving area and volume models, such as persons per square mile. Understand density as a ratio. Differentiate between area and volume densities, their units, and situations in which they are appropriate (e.g., area density is ideal for measuring population density spread out over land, and the concentration of oxygen in the air is best measured with volume density). |
Explore design problems that exist in local communities, such as building a shed with maximum capacity in a small area or locating a hospital for three communities in a desirable area. Geometry Problem Solving https://map.mathshell.org/materials/lessons.php?taskid=216&subpage=concept |
|
https://abspd.appstate.edu/node/377 accessed 1/4/2015 |
||
, for the volume of a cone, where B is the area of the base and H is the height of the. If a cone is inside a cylinder with a diameter of 12in. and a height of 16 in., find the volume of the cone.